The independence ratio of 4-cycle-free planar graphs

05/03/2023

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by   Tom Kelly, et al.

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We prove that every n-vertex planar graph G with no triangle sharing an edge with a 4-cycle has independence ratio n/α(G) ≤ 4 - ε for ε = 1/30. This result implies that the same bound holds for 4-cycle-free planar graphs and planar graphs with no adjacent triangles and no triangle sharing an edge with a 5-cycle. For the latter case we strengthen the bound to ε = 2/9.